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1 results

  • Comparison theorem and stability under perturbation of transition rate matrices for regime-switching processes

  • Part of
  • Jinghai Shao
  • Journal:
    Journal of Applied Probability / Volume 61 / Issue 2 / June 2024
    Published online by Cambridge University Press:
    14 September 2023, pp. 540-557
    Print publication:
    June 2024
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  • A comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to pathwise-control the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp estimate on the stability of Markovian regime-switching processes under the perturbation of transition rate matrices is provided. Our approach is based on elaborate constructions of switching processes in the spirit of Skorokhod’s representation theorem varying according to the problem being dealt with. In particular, this method can cope with switching processes in an infinite state space and not necessarily of birth–death type. As an application, some known results on the ergodicity and stability of state-dependent regime-switching processes can be improved.